Nuclear reactions are completely independent of chemical reactions, in the sense that nuclear energies are several orders of magnitude larger. Thus an atom which has undergone a nuclear reaction reacts the same chemically as an identical atom which has not.
There are four major types of nuclear reaction:
n + 235U -> 141Ba + 92Kr + 3n,where the superscripts indicate the nucleon numbers (denoted by A). Equal to the sum of the numbers of protons and neutrons in the nucleus, A is also approximately equal to the atomic mass, when mass is measured in atomic mass units (1.66055 * 10-27 kg). When sufficient amounts of Uranium are present, the extra neutrons may initiate additional fission reactions, leading to a chain reaction.
This reaction produces approximately 188 MeV of excess kinetic energy, accounting for its explosive potential. It is a prime example of the the scaling relationship mentioned in the last section: smaller sources are associated with larger energies.
p + p -> 2H + e+ + ν + .42 MeV.Here ν denotes a neutrino: a neutral and nearly massless counterpart to the electron. Neutrinos interact via the weak force: trillions pass through you each second without any reaction at all with the atoms in your body! The weak force is qualitatively different from electromagnetism, gravity and the strong force. It is called the weak force because it is weaker by a factor of 10000 than the strong force, although it is not the weakest: gravity is 1036 times weaker. Gravity only appears to be so strong because of the sizes of the sources of the gravitational field: planets, stars and galaxies.
The e+ denotes a positron: a particle of antimatter. An antiparticle is identical to its ordinary "partner" (in this case an electron) in every way except its charge and helicity (whether its spin is parallel or antiparallel to its momentum). The positron is created in order to conserve charge, and the neutrino is necessary to "balance" the creation of the positron.
Electrons, positrons and neutrinos are collectively called leptons. There were no leptons on the left hand side of the fusion reaction, so there must be none on the right: the positron, with lepton number -1, plus the neutrino, with lepton number 1, add up to 0 leptons.Leptons cannot interact via the strong force, although those which have electric charge can interact electromagnetically. And in perhaps one of the most bizarre mysteries in physics, only left-handed leptons (those whose spin is parallel to their momentum) can interact via the weak force. Right-handed leptons, with negative helicity, are weakly sterile, as are right-handed quarks
Quarks and leptons are fermions, which obey the Pauli Exclusion Principle: no two can have the same quantum numbers and be in the same place at the same time. Bosons do not suffer this same restriction. In addition, fermions have spin 1/2 while bosons have spin 1.The extra energy that is released in this reaction comes from the fact that the combined mass of the products is lower than the combined mass of the reactants. This mass difference is equivalent to energy through Einstein's famous equation
E = m c2and comes about because the binding energy of the resulting Deuterium nucleus (2H) is negative. Differences in binding energies also accounts for the excess energy released in fission.
Note that fission and neutron capture start out the same; the difference in fission is that the excited nucleus (with the extra neutron) is too unstable to stay together. In neutron capture, the new nucleus is simply radioactive, that is, it decays in one of the following modes:
the transformation of a neutron into a proton (a down quark into an up quark), with the emission of an electron for charge conservation, and an antineutrino for lepton conservation; orBeta decay occurs in those situations in which alpha decay would leave the nucleus less stable than it was before.the transformation of a proton into a neutron plus a positron and a neutrino.
Neutrinos and antineutrinos are very difficult to detect: experiments can typically detect only one in 1015! Their existence was first predicted to account for missing energy and momentum in beta decays.
Three such series occur naturally, one beginning with 232Th90, and the others beginning with 238U92 and 235U92. The Thorium Series is
β + 228Ac89 ->
β + 228Th90 ->
α + 224Ra88 ->
α + 220Rn86 ->
α + 216Po84 ->
β + 216At85 (.013% of the time) ->
β + 212Po84 (66.3% of the time) ->
We suggest the construction of the 238U 92 series as an exercise for the reader.
It includes the following intermediate isotopes: 210Bi, 214Bi, 234Pa,
210Pb, 214Pb, 210Po, 214Po, 218Po, 226Ra,
222Rn, 230Th, 234Th, 210Tl and 234U, and ends with
206Pb. In all of the beta decays Z -> Z + 1. Note that there is a branch in this series.
The following applet knows all of the alpha and electron-beta decay modes for the currently known elements. It will give you an isotope and the decay mode, and you must compute Z, A and N for the decay product. All answers must be exact! You may find it useful to refer to the Periodic Table of the Elements.
In a large population of unstable nuclei, the decays occur apparently at random, but since the decay rate is proportional to the number of nuclei present, the overall decay rate is described by an
exponential function
232Th90 ->
The branches in the decay series occur when two decay modes are possible with (usually) differing probabilities. We can never tell for certain when any given nucleus will decay, and if a branch is possible, which branch it will take when it does decay. For this reason, radioactive decay rates are based on large samples (numbers on the order of Avogadro's number).
α + 228Ra88 ->
α + 212Pb82 (99.987% of the time) ->
with the 212Bi83 ->
β + 212Bi83
or
α + 212Bi83,
α + 208Tl81 (33.7% of the time) ->
β + 208Pb82
or
α + 208Pb82.
D = D0 2 - t / τ.
Here D0 is the initial amount of the parent nucleus, D is the amount left at time t,
and since the base for the exponential is 2, τ is a half-life
(the time it takes for D to be 1/2 of D0). The half life is proportional to the stability of the excited nucleus:
more stable nuclei have longer half lives, etc. It is analogous to the time constant in an RC circuit:
it is a characteristic value for a given isotope. D may be measured in units of mass, but is often measured in Curies
(Ci, corresponding to about 1g of Ra, or about 3.7 * 1010 decays/s). Half lives from the Thorium Series are
Biological organisms are affected by exposure to radioactivity. Low velocity alpha particles are more destructive since they tend to interact more
often than high velocity beta particles. A mitigating effect occurs when radioactive atoms are metabolized within the body.
The radioactive decay mode provides a "physical" half-life, and the metabolic process provides a "biological" half-life.
The two act as parallel paths for elimination of the radioactivity, and in analogy with
parallel resistors, the effective half life is then
232Th90 1.405 * 1010 years 228Ra88 5.75 years 228Ac89 6.15 hours 228Th90 1.9131 years 224Ra88 3.66 days 220Rn86 55.6 seconds 216Po84 0.145 seconds 212Pb82 10.64 hours 212Bi83 25 / 60.55 minutes 216At85 0.33 milliseconds 208Tl81 3.053 minutes 212Po84 45.1 seconds
1 / τeffective = 1 / τphysical + 1 / τbiological.This is the last section of the text. We hope you have enjoyed learning about the applications of physics to some of the topics in biology and chemistry which interest you most, and that you will find both the information you have learned and the thought processes you've developed useful in your future academic and professional career. We wish you the best of luck!
©2013, Kenneth R. Koehler. All Rights Reserved. This document may be freely reproduced provided that this copyright notice is included.
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